Set an oven rack about 6 inches from the heat source and preheat the oven’s broiler.

Heat oil and butter in a skillet over medium heat. Add chicken breasts; cook until no longer pink on the inside and golden brown on the outside, seasoning each side with Creole seasoning, about 10 minutes per side.

Scoop avocados into a bowl. Add tomato, onion, lime juice, garlic powder, salt, and black pepper; mash together.

Spoon about 1/3 cup guacamole onto each chicken breast, top with 1 slice pepper Jack cheese; broil until cheese is melted and bubbling, 2 to 4 minutes.